Antieigenvalue bounds

Antieigenvalue inequalities in operator theory

“…The author and Gustafson have studied µ 1 (T ) and |µ 1 |(T ) for normal operators on finite-and infinite-dimensional spaces (see [9,10,12,13]). Also, in [11], the author has studied µ 1 (T , S), where S and T are two operators belonging to the same closed normal subalgebra of B(H).…”

Application of the Two Nonzero Component Lemma in Resource Allocation

“…It was in his investigation on problems of antieigenvalue theory that the author discovered and proved the Two Nonzero Component Lemma (see [2]- [4]). Although this lemma is utilized effectively by the author in matrix theory, it is by nature a dimension reducing optimization lemma which has potential applications in all areas of mathematics and physics.…”

“…In the proof of the TNCL in [2] and [3] we took advantage of the facts that the set In the following sections we will use GTNCL to compute a closed form answer for the distribution of the search effort problem.…”

Proving and Extending Greub-Reinboldt Inequality Using the Two Nonzero Component Lemma

“…In his investigation on problems of antieigenvalue theory the author has discovered a useful lemma which he calls it the Two Nonzero Component Lemma (see [4]- [6]). Although this Lemma is implicitly used in all of the papers just cited, it was not until 2008 that he stated a formal description of the Lemma in his paper titled, "Antieigenvalue Techniques in Statistics".…”